Question

ABC is a right angled triangle. All the measurements are in cm.

Answer 1

Step-by-step explanation:

By Pythagoras' Theorem,

we have x² + (x + 2)² = (x + 4)².

=> 2x² + 4x + 4 = x² + 8x + 16

=> x² - 4x - 12 = 0

(The constants are a = -4, b = -12)

=> (x - 6)(x + 2) = 0

=> x = 6 or x = -2

The value x = -2 is rejected as side lengths cannot be negative.

Hence we have x = 6.

=> AB = 6cm, BC = 8cm, AC = 10cm.

P.S. What you see above is the full solution. You just need to type x² - 4x - 12 = 0 in the blank.